White teenagers are far more likely to smoke than their minority ethnic counterparts, Roma children are falling well behind their peers at school and black men face the highest likelihood of being found guilty in court.

Those are just some of the issues that will be highlighted in a government audit on race equality that will reveal deeply ingrained disparities across the country when it is published on Tuesday.

Much of the data shows disadvantage for black and ethnic minority communities and there is a postcode lottery in school performance.

But it also makes clear that among the poorest children in the country, white British pupils do worst at school. Among that group, just 32% reach the expected standard of reading, writing and maths at 11.

Theresa May has said she wants the findings – which shine a light on vastly different experiences for ethnic groups in Britain’s schools, workplaces, hospitals and justice system, and reveal huge regional disparities – to reveal “uncomfortable truths”.

She said: “People who have lived with discrimination don’t need a government audit to make them aware of the scale of the challenge. But this audit means that for society as a whole – for government, for our public services – there is nowhere to hide. These issues are now out in the open. And the message is very simple: if these disparities cannot be explained then they must be changed.”

Communities secretary Sajid Javid the data would not provide the answers to why disparity existed, but said the government wanted to work with outside groups to come up with ways it could tackle the injustice.

“We are not pretending today we are sitting here with all the answers, some of them might have a rational explanation but others will require action,” he told BBC Radio 4’s Today. “There are hundreds of thousands of Pakistani or Bangladeshi women who don’t speak proper English or hardly speak it at all.

“That might be through choice in some cases, a cultural issue. But it is a big issue because it does then hold those women back from the employment market and other opportunities.”

Javid said he would address some of the problems, including English language issues, when his department publishes a new integration strategy. “I think there will be many people out there today listening to this, taking notice, and thinking this is just the kind of thing we want our government to do,” he said. “That means where there are injustices, we are doing everything we can to tackle them and reveal them.”

The figures come alongside new research that suggests minority ethnic women are being hardest hit by austerity. The report by the Runnymede Trust and Women’s Budget Group claims black and Asian households have faced the biggest drop in living standards, of 19.2% and 20.1% respectively. That amounts to a real-terms average annual loss of £8,407 and £11,678.

Other findings, which include known data presented in a new manner alongside unpublished information in 24 areas, are:

Black Caribbean pupils are permanently excluded from school at three times the rate of white British pupils – triggering a Department for Education review.

Almost nine out of 10 white Gypsy and Roma children do not reach the expected standard for reading, writing and maths at 11.

9.2% of white 15-year-olds smoked in 2014-15, almost four times the proportion of black teenagers (2.4%).

Black men are more likely to be found guilty at crown court, with 112 sentenced to custody for every 100 white men.

Employment rates are higher for white people than ethnic minorities across the country, but the gap in the north (13.6%) is significantly wider than that in the south (9%).

The data goes beyond breaking down figures by colour, delving into differences between a variety of ethnic groups. Chinese pupils excelled at primary school, with 71% reaching the expected standard for reading, writing and maths, compared with 65% of children from an Indian background, 54% of white British pupils, 51% of black children, and 13% of white Gypsy and Traveller children.

Officials said one of the big surprises of the findings was the large regional disparities. As well as bigger gaps for employment in the north, there were big differences in schooling.

More than three-quarters of black children reached expected levels in Sunderland and Gateshead (although the overall numbers were low), compared with less than a quarter in Stockport, laying bare a postcode lottery in schooling.

Areas with larger minority ethnic populations and with strong performances among black children included Kensington and Chelsea and Greenwich in London.

The government said the data would affect policy, with the Department for Work and Pensions taking action in 20 targeted hotspots to help people from minority ethnic backgrounds into work with mentoring schemes and traineeships.

There will also be recommendations taken up from the Labour MP David Lammy’s review of the justice system, including performance indicators within prisons to assess outcomes for different ethnic groups.

Lammy told the Guardian: “We simply can’t let this racial disparity audit bring forth more talking shops. We’ve had a lot of talk, it’s now time for action.”

Omar Khan, director of the Runnymede Trust, said: “Once the details of the audit are digested, we want to see a comprehensive and government-wide plan with the goal of eliminating racial barriers in a generation.”

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